MATHEMATICS 29 



FORMULAS 



A formula is a brief statement of a rule, in which letters or 

 other symbols are used to denote the different quantities 

 involved. For example, the rule for finding the volume of a 

 rectangular prism is as follows: The volume of a rectangular 

 prism is equal to the product of the length, width, and height of 

 the prism. If the dimensions of the prism are taken in inches, 

 the volume will be in cubic inches; if they are taken in feet, 

 the volume will be in cubic feet; and so on. Suppose, however, 

 that the volume is denoted by v, the length by I, the width 

 by w, and the height by h. Then, the foregoing rule may 

 be stated much more simply and concisely by the formula 

 v = lXwXh. This formula indicates that the volume v is 

 equal to the product of the length I, the width w, and the height 

 h of the prism. Where several letters are multiplied together 

 in a formula, it is customary to omit the multiplication signs, 

 the multiplication then being taken for granted. The fore- 

 going formula, therefore, would ordinarily be written v = lwh, 

 The multiplication sign must not be omitted between numbers 

 that are to be multiplied together. 



As may be seen from the example just given, a formula 

 consists of two parts separated by the sign of equality. The 

 letters or symbols denoting the quantities that are known are 

 usually placed at the right of the equality sign, and the letter 

 or symbol designating the value to be found is placed at the 

 left of the equality sign. To apply a formula to the solution 

 of an example a numerical value is substituted for each letter 

 that denotes a known quantity, and the indicated mathematical 

 operations are then performed. Care must be observed, in 

 using a formula, to have all weights, dimensions, or other 

 values expressed in the units required by the formula. 



Letters with additional marks, such as O ', a", di, T a , etc., 

 are often found in formulas when similar quantities are to be 

 represented by the same letter and yet to be distinguished 

 from one another. The marks ' " are termed prime and 

 second, respectively, and the marks i and a are termed sub- 

 scripts or subs. The four examples just given are read large 

 C prime, a second, d sub one, and large T sub a. Parentheses 

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